Green's function for two-interval Sturm-Liouville problems

Aiping Wang, Anton Zettl
Abstract:
We construct the Green's function and the characteristic function for
two-interval regular Sturm-Liouville problems with separated and coupled,
self-adjoint and non-self-adjoint, boundary conditions. In the self-adjoint
case these problems may have boundary conditions requiring jump
discontinuities of the eigenfunctions or their derivatives. Such conditions
are known by various names including transmission and interface conditions
and have been studied by many authors in the recent literature.